This is my non-native opinion: ”Surf” and ”browse” can be used interchangeably (except that browse sounds a bit more serious/formal than ”surf”) and mean to look at (and for) content on the internet. Navigate has to do with how you actually find that information/content and move around on a website. Like, ”this website is very unintuitive and difficult to navigate”.

I think they are interchangeable. "Browse" is the most neutral. It is also the oldest term. It is older than the Web. The idea is that you do not "read" hypertext, you "browse" it. "Surf" suggests browsing the web for pleasure. "Navigate" suggests trying to locate specific information. As evidence that they are interchangeable, "Netscape Navigator" was the name of an important early graphical "web browser." And today, Apple combines the ideas of "surfing" in the name of its web browser, Safari (surfers call a surfing trip a "safari"), and "navigation" in the icon, which represents a navigational compass. Historical note: "Browsing" once meant to read a books in a library out of sequence, jumping back and forth, a bit here and a bit there, as one idea suggested another. "Browse," "browser," and "browsery" were used in 1965 in the INTREX conference, devoted to the potential uses of computer technology in libraries, and later adopted to refer to hypertext access software. The World Wide Web described its linkage system as "hypertext." The idea of its being world wide, with links connecting and jumping back and forth from continent to continent, brought in the idea of navigation.